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We study the effects of nonlocal control of pulse propagation in excitablemedia. As a generic example for an excitable medium the FitzHugh-Nagumo modelwith diffusion in the activator variable is considered. Nonlocal coupling inform of an integral term with a spatial kernel is added. We find that thenonlocal coupling modifies the propagating pulses of the reaction-diffusionsystem such that a variety of spatio-temporal patterns are generated includingacceleration, deceleration, suppression, or generation of pulses, multiplepulses, and blinking pulse trains. It is shown that one can observe theseeffects for various choices of the integral kernel and the coupling scheme,provided that the control strength and spatial extension of the integral kernelis appropriate. In addition, an analytical procedure is developed to describethe stability borders of the spatially homogeneous steady state in controlparameter space in dependence on the parameters of the nonlocal coupling.

Nonlocal control of pulse propagation in excitable media